The first section covers the foundations of probability in measure theoretic terms. i.e events in probability as measurable sets, random variables as measurable functions, expectation as integration with respect to the probability measure etc. My only criticism is Chapter 8 on product measure could do with more explanation and examples. The second section in my […]

# Probability

## ABRACADABRA: Part 3 (Comment)

A colleague of mine asked me what if we wanted to know the expected time for the monkey to type the sequence of letters ABCDEFGHIJK and not ABRACADABRA what would the result be. Trudging through the mathematics gives \( \mathbb E[T] =26^{11} \). Why is the expected time for the monkey to type ABRACADABRA longer […]

## ABRACADABRA: Part 2

To answer the question what is the expected time for a monkey to type ABRACADABRA, assuming he types the letters of the alphabet randomly at times 1,2,3,… rigorously we will need to use a theorem from discrete martingale theory, Doob’s Optional Stopping Theorem. This theorem states sufficient conditions for a stopped martingale to have the […]

## ABRACADABRA: Part 1

Since I have just reviewed ‘Probability with Martingales’ I thought it would be nice to add one of the most famous puzzles in the book to the puzzles page. If at each of times 1,2,3,.. a monkey types a capital letter at random. What is the expected time for the monkey to first produce the letters […]

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